Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3); (5)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) y, -x, -z | (4) -y, x, -z | | (5) -x + 1/2, y + 1/2, -z | (6) x + 1/2, -y + 1/2, -z | (7) -y + 1/2, -x + 1/2, z | (8) y + 1/2, x + 1/2, z |
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I Maximal translationengleiche subgroups
| [2] P-411 (81, P-4) | 1; 2; 3; 4 |
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| [2] P21m (35, Cmm2) | 1; 2; 7; 8 | a - b, a + b, c
| 0, 1/2, 0
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| [2] P2211 (18, P21212) | 1; 2; 5; 6 |
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II Maximal klassengleiche subgroups
[2] c' = 2c
| P-421c (114) | <2; 3; 5 + (0, 0, 1)> | a, b, 2c | |
| P-421c (114) | <2; 5; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P-421m (113) | <2; 3; 5> | a, b, 2c | |
| P-421m (113) | <2; (3; 5) + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[3] c' = 3c
 | P-421m (113) | <2; 3; 5> | a, b, 3c | | | P-421m (113) | <2; (3; 5) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P-421m (113) | <2; (3; 5) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| P-421m (113) | <2; (3; 5) + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p2] a' = pa, b' = pb
| P-421m (113) | <2 + (2u, 2v, 0); 3 + (u - v, u + v, 0); 5 + (p/2 - 1/2 + 2u, p/2 - 1/2, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [2] P4/mbm (127); [2] P4/nmm (129); [2] P42/mnm (136); [2] P42/ncm (138) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] C-42m (115, P-4m2); [2] I-42m (121) |
